Observer-based controller designs are presented that are robust to failures from a preselected set of sensors or actuators for both centralized and decentralized systems. The designs guarantee stability and an $H\sb\infty$-norm bound on the closed-loop system despite failures in any subset of that preselected set of sensors or actuators. The discrete-time divided-difference operator formulation facilitates the solution of three problems: the unification of discrete- and continuous-time results for sampled-data systems, providing a numerical method for solving the decentralized discrete-time design equation; the design of sampled-data decentralized controllers that bound the continuous-time closed-loop system norm; and the design of multirate decentralized digital controllers for systems with sensors and actuators operating at different sampling and zero-order-hold rates.